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3 years ago

64x squared y cubed + 8xy divided by 4xy squared

Mathematics

1 answer:

Vinil7 [7]3 years ago

3 0

Answer:

2x^2y^2*(32y+1)

Step-by-step explanation:

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The function g is a transformation of f. If g has a y-intercept at -1, which of the following functions could represent g?

scZoUnD [109]

The answer is C. G(x)= f(x) -1

4 0

3 years ago

Solve the equation on the interval [0,2π]

WARRIOR [948]

$\bf 16sin^5(x)+2sin(x)=12sin^3(x)
\\\\\\
16sin^5(x)+2sin(x)-12sin^3(x)=0
\\\\\\
\stackrel{common~factor}{2sin(x)}[8sin^4(x)+1-6sin^2(x)]=0\\\\
-------------------------------\\\\
2sin(x)=0\implies sin(x)=0\implies \measuredangle x=sin^{-1}(0)\implies \measuredangle x=
\begin{cases}
0\\
\pi \\
2\pi 
\end{cases}\\\\
-------------------------------$

$\bf 8sin^4(x)+1-6sin^2(x)=0\implies 8sin^4(x)-6sin^2(x)+1=0$

now, this is a quadratic equation, but the roots do not come out as integers, however it does have them, the discriminant, b² - 4ac, is positive, so it has 2 roots, so we'll plug it in the quadratic formula,

$\bf 8sin^4(x)-6sin^2(x)+1=0\implies 8[~[sin(x)]^2~]^2-6[sin(x)]^2+1=0
\\\\\\
~~~~~~~~~~~~\textit{quadratic formula}
\\\\
\begin{array}{lcccl}
& 8 sin^4& -6 sin^2(x)& +1\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array} 
\qquad \qquad 
sin(x)= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}
\\\\\\
sin(x)=\cfrac{-(-6)\pm\sqrt{(-6)^2-4(8)(1)}}{2(8)}\implies sin(x)=\cfrac{6\pm\sqrt{4}}{16}
\\\\\\
sin(x)=\cfrac{6\pm 2}{16}\implies sin(x)=
\begin{cases}
\frac{1}{2}\\\\
\frac{1}{4}
\end{cases}$

$\bf \measuredangle x=
\begin{cases}
sin^{-1}\left( \frac{1}{2} \right)
sin^{-1}\left( \frac{1}{4} \right)
\end{cases}\implies \measuredangle x=
\begin{cases}
\frac{\pi }{6}~,~\frac{5\pi }{6}\\
----------\\
\approx~0.252680~radians\\
\qquad or\\
\approx~14.47751~de grees\\
----------\\
\pi -0.252680\\
\approx 2.88891~radians\\
\qquad or\\
180-14.47751\\
\approx 165.52249~de grees
\end{cases}$

3 0

3 years ago

Which statement is true about the function f(x)= squared root negative x?

Liono4ka [1.6K]

The answer is the first option: it has the same domain as the function f(x) = - √(-x).

The domain is the set of x-values for which the function is defined.

The square root function is defined only for zero and positve values.

- x is positive when x negative.

So the domain for - √(-x) and √(-x) are the same: x less than or equal to zero.

4 0

2 years ago

The solid figire shown consists of a cylinder and a cone

mariarad [96]

Sorry
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8 0

3 years ago

Find the volume of soup can if the diameter is 6.5 in and the height is 9 in

Nitella [24]

Answer:

V =298.49625 in^3

Step-by-step explanation:

Volume of a cylinder is given by

V = pi * r^2 *h

We know the diameter so we can find the radius

r = d/2 =6.5/2 = 3.25

and we know the height =9

V = pi * (3.25)^2 *9

V = pi*95.0625

If we approximate by 3.14

V = 3.14*95.0625

V =298.49625 in^3

5 0

3 years ago

Read 2 more answers